From c5259532af8fb8ae726ecea102447f068ac7a33f Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Wed, 16 Aug 2023 14:55:59 -0700 Subject: [PATCH 01/15] Add single-qubit wire cutting how-to, and `expand_observables` function --- circuit_knitting/cutting/__init__.py | 4 +- circuit_knitting/cutting/cut_wire_to_move.py | 66 ++- docs/circuit_cutting/how-tos/README.rst | 2 + .../how-tos/how_to_specify_cut_wires.ipynb | 403 ++++++++++++++++++ test/cutting/test_cut_wire_to_move.py | 79 +++- 5 files changed, 549 insertions(+), 5 deletions(-) create mode 100644 docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb diff --git a/circuit_knitting/cutting/__init__.py b/circuit_knitting/cutting/__init__.py index 462bcb8eb..1bf74b68c 100644 --- a/circuit_knitting/cutting/__init__.py +++ b/circuit_knitting/cutting/__init__.py @@ -22,6 +22,7 @@ :nosignatures: transform_cuts_to_moves + expand_observables partition_circuit_qubits partition_problem cut_gates @@ -87,7 +88,7 @@ ) from .cutting_evaluation import execute_experiments, CuttingExperimentResults from .cutting_reconstruction import reconstruct_expectation_values -from .cut_wire_to_move import transform_cuts_to_moves +from .cut_wire_to_move import transform_cuts_to_moves, expand_observables __all__ = [ "partition_circuit_qubits", @@ -99,4 +100,5 @@ "PartitionedCuttingProblem", "CuttingExperimentResults", "transform_cuts_to_moves", + "expand_observables", ] diff --git a/circuit_knitting/cutting/cut_wire_to_move.py b/circuit_knitting/cutting/cut_wire_to_move.py index a1039b7a2..06824682c 100644 --- a/circuit_knitting/cutting/cut_wire_to_move.py +++ b/circuit_knitting/cutting/cut_wire_to_move.py @@ -14,11 +14,15 @@ from __future__ import annotations from itertools import groupby +import numpy as np + from qiskit.circuit import Qubit, QuantumCircuit +from qiskit.circuit.exceptions import CircuitError +from qiskit.quantum_info import PauliList from circuit_knitting.cutting.instructions.move import Move -def transform_cuts_to_moves(circuit: QuantumCircuit) -> QuantumCircuit: +def transform_cuts_to_moves(circuit: QuantumCircuit, /) -> QuantumCircuit: """Transform all :class:`.CutWire` instructions in a circuit to :class:`.Move` instructions. Args: @@ -82,3 +86,63 @@ def _circuit_structure_mapping( new_circuit.add_register(creg) return new_circuit, mapping + + +def expand_observables( + observables: PauliList, + original_circuit: QuantumCircuit, + final_circuit: QuantumCircuit, + /, +) -> PauliList: + """Expand observable(s) according to the qubit mapping between ``original_circuit`` and ``final_circuit``. + + The qubits on ``final_circuit`` must be a superset of those on + ``original_circuit``. + + Given a :class:`.PauliList` of observables, this function returns new + observables with identity operators placed on the qubits that did not + exist in ``original_circuit``. This way, observables on + ``original_circuit`` can be mapped to appropriate observables on + ``final_circuit``. + + This function is designed to be used after calling ``final_circuit = + transform_cuts_to_moves(original_circuit)`` (see + :func:`.transform_cuts_to_moves`). + + This function requires ``observables.num_qubits == + original_circuit.num_qubits`` and returns new observables such that + ``retval.num_qubits == final_circuit.num_qubits``. + + Args: + observables: Observables corresponding to ``original_circuit`` + original_circuit: Original circuit + final_circuit: Final circuit, whose qubits the original ``observables`` should be expanded to. + + Returns: + New observables, appropriate for the ``final_circuit``. + + Raises: + ValueError: ``observables`` and ``original_circuit`` have different number of qubits. + ValueError: Qubit from ``original_circuit`` cannot be found in ``final_circuit``. + """ + if observables.num_qubits != original_circuit.num_qubits: + raise ValueError( + "The `observables` and `original_circuit` must have the same number " + f"of qubits. ({observables.num_qubits} != {original_circuit.num_qubits})" + ) + mapping: list[int] = [] + for i, qubit in enumerate(original_circuit.qubits): + try: + idx = final_circuit.find_bit(qubit)[0] + except CircuitError as ex: + raise ValueError( + f"The {i}-th qubit of the `original_circuit` cannot be found " + "in the `final_circuit`." + ) from ex + mapping.append(idx) + dims = (len(observables), final_circuit.num_qubits) + z = np.full(dims, False) + x = np.full(dims, False) + z[:, mapping] = observables.z + x[:, mapping] = observables.x + return PauliList.from_symplectic(z, x, observables.phase.copy()) diff --git a/docs/circuit_cutting/how-tos/README.rst b/docs/circuit_cutting/how-tos/README.rst index 83025824d..b19b5325a 100644 --- a/docs/circuit_cutting/how-tos/README.rst +++ b/docs/circuit_cutting/how-tos/README.rst @@ -6,3 +6,5 @@ Circuit Cutting How-Tos exact quasi-distributions for circuits containing mid-circuit measurements. - `Generate exact sampling coefficients `__: Generate exact sampling coefficients and run all unique samples from the distribution. +- `Specify cut wires as a single-qubit instruction `__: + Perform wire cutting with a single-qubit `CutWire` instruction, rather than a two-qubit `Move` operation. diff --git a/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb new file mode 100644 index 000000000..3e7467ca7 --- /dev/null +++ b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb @@ -0,0 +1,403 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "b04b8bc7", + "metadata": {}, + "source": [ + "# How to place wire cuts using a single-qubit `CutWire` instruction\n", + "\n", + "This how-to guide is intended to demonstrate how to place wire cuts using single-qubit `CutWire` instructions, which may at times be more convenient than specifying them as two-qubit `Move` instructions." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "1aa871cb", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from qiskit import QuantumCircuit\n", + "from qiskit.quantum_info import PauliList\n", + "from qiskit_aer.primitives import Estimator, Sampler\n", + "\n", + "from circuit_knitting.cutting import (\n", + " partition_problem,\n", + " execute_experiments,\n", + " reconstruct_expectation_values,\n", + ")\n", + "\n", + "from circuit_knitting.cutting.instructions import CutWire\n", + "from circuit_knitting.cutting import transform_cuts_to_moves, expand_observables" + ] + }, + { + "cell_type": "markdown", + "id": "06ae4c39", + "metadata": {}, + "source": [ + "### Prepare a circuit for cutting\n", + "\n", + "As in the [tutorial for wire cutting](../tutorials/03_wire_cutting_via_move_instruction.ipynb), we have used a circuit inspired by Fig. 1(a) of arXiv:2302.03366v1. The cut locations are marked manually here with `CutWire` instructions." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "0ae22516", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc_0 = QuantumCircuit(7)\n", + "for i in range(7):\n", + " qc_0.rx(np.pi / 4, i)\n", + "qc_0.cx(0, 3)\n", + "qc_0.cx(1, 3)\n", + "qc_0.cx(2, 3)\n", + "qc_0.append(CutWire(), [3])\n", + "qc_0.cx(3, 4)\n", + "qc_0.cx(3, 5)\n", + "qc_0.cx(3, 6)\n", + "qc_0.append(CutWire(), [3])\n", + "qc_0.cx(0, 3)\n", + "qc_0.cx(1, 3)\n", + "qc_0.cx(2, 3)\n", + "qc_0.draw(\"mpl\")" + ] + }, + { + "cell_type": "markdown", + "id": "7ee07a81", + "metadata": {}, + "source": [ + "### Recover the uncut circuit\n", + "\n", + "`CutWire` instructions decompose to nothing (they are equivalent to the identity), so the uncut circuit can be recovered as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "631286a6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc_0.decompose(\"cut_wire\").draw(\"mpl\")" + ] + }, + { + "cell_type": "markdown", + "id": "dcd8dea0", + "metadata": {}, + "source": [ + "### Specify some observables\n", + "\n", + "These observables have 7 qubits, just like the original circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "847a3205", + "metadata": {}, + "outputs": [], + "source": [ + "observables_0 = PauliList([\"ZIIIIII\", \"IIIZIII\", \"IIIIIIZ\"])" + ] + }, + { + "cell_type": "markdown", + "id": "59730746", + "metadata": {}, + "source": [ + "### Transform cuts to moves\n", + "\n", + "The next step is to transform each `CutWire` into a `Move`. An additional qubit is added to the circuit for each `CutWire` in the input circuit.\n", + "\n", + "Notice that, unlike in the [wire cutting tutorial](../tutorials/03_wire_cutting_via_move_instruction.ipynb), this function does not result in the _re_-use of a qubit. Because any method for qubit re-use is based on heuristics, this function naively allocates an additional qubit for each cut. Users wishing to re-use qubits might wish to experiment with [qiskit-qubit-reuse](https://github.com/qiskit-community/qiskit-qubit-reuse)." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "e4ee1559", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc_1 = transform_cuts_to_moves(qc_0)\n", + "qc_1.draw(\"mpl\")" + ] + }, + { + "cell_type": "markdown", + "id": "c22b9572", + "metadata": {}, + "source": [ + "### Update the observables\n", + "\n", + "The transformed circuit contains additional qubits (one for each `CutWire` instruction), so the observables must be updated for the new circuit. This can be done using the `expand_observables` function.\n", + "\n", + "The resulting observables have 9 qubits, just like the transformed circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "95fbeda0", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "PauliList(['ZIIIIIIII', 'IIIZIIIII', 'IIIIIIIIZ'])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "observables_1 = expand_observables(observables_0, qc_0, qc_1)\n", + "observables_1" + ] + }, + { + "cell_type": "markdown", + "id": "6f64acd6", + "metadata": {}, + "source": [ + "### Separate the circuit and observables\n", + "\n", + "In order to partition the circuit, we must specify `partition_labels` based on the connectivity of the circuit. In the future, we expect to provide a way for this to be determined automatically, as it is technically redundant with the information contained by the original circuit with `CutWire` instructions (see PR [#367](https://github.com/Qiskit-Extensions/circuit-knitting-toolbox/pull/367))." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "99bef123", + "metadata": {}, + "outputs": [], + "source": [ + "subcircuits, bases, subobservables = partition_problem(\n", + " circuit=qc_1, partition_labels=\"AAAABABBB\", observables=observables_1\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "ce2bf0cd", + "metadata": {}, + "source": [ + "From here forward, the cutting workflow is the same as usual, but the remaining steps are spelled out here explicitly so one can follow along with the results." + ] + }, + { + "cell_type": "markdown", + "id": "bae9ac63", + "metadata": {}, + "source": [ + "### Visualize the decomposed problem\n", + "\n", + "Notice that once the circuits have been cut, some of the instructions are able to commute past each other. For instance, in subcircuit \"A\", half of the second `Move` operation is actually the _first_ operation on the final qubit." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "abeee650", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'A': PauliList(['IIIII', 'ZIIII', 'IIIIZ']),\n", + " 'B': PauliList(['ZIII', 'IIII', 'IIII'])}" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "subobservables" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "aaef5b3d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "subcircuits[\"B\"].draw(\"mpl\")" + ] + }, + { + "cell_type": "markdown", + "id": "2e02632b", + "metadata": {}, + "source": [ + "### Generate and run the cutting experiments; reconstruct and compare against uncut expectation values" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "459dcee8", + "metadata": {}, + "outputs": [], + "source": [ + "quasi_dists, coefficients = execute_experiments(\n", + " circuits=subcircuits,\n", + " subobservables=subobservables,\n", + " num_samples=np.inf,\n", + " samplers=Sampler(run_options={\"shots\": 2**12}),\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "e317a998", + "metadata": {}, + "outputs": [], + "source": [ + "reconstructed_expvals = reconstruct_expectation_values(\n", + " quasi_dists,\n", + " coefficients,\n", + " subobservables,\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "5ae568ca", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Reconstructed expectation values: [0.16293341, 0.69796044, 0.71675336]\n", + "Exact expectation values: [0.1767767, 0.70710678, 0.70710678]\n", + "Errors in estimation: [-0.01384329, -0.00914634, 0.00964658]\n", + "Relative errors in estimation: [-0.07830945, -0.01293488, 0.01364233]\n" + ] + } + ], + "source": [ + "estimator = Estimator(run_options={\"shots\": None}, approximation=True)\n", + "exact_expvals = (\n", + " estimator.run([qc_0] * len(observables_0), list(observables_0)).result().values\n", + ")\n", + "print(\n", + " f\"Reconstructed expectation values: {[np.round(reconstructed_expvals[i], 8) for i in range(len(exact_expvals))]}\"\n", + ")\n", + "print(\n", + " f\"Exact expectation values: {[np.round(exact_expvals[i], 8) for i in range(len(exact_expvals))]}\"\n", + ")\n", + "print(\n", + " f\"Errors in estimation: {[np.round(reconstructed_expvals[i]-exact_expvals[i], 8) for i in range(len(exact_expvals))]}\"\n", + ")\n", + "print(\n", + " f\"Relative errors in estimation: {[np.round((reconstructed_expvals[i]-exact_expvals[i]) / exact_expvals[i], 8) for i in range(len(exact_expvals))]}\"\n", + ")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/test/cutting/test_cut_wire_to_move.py b/test/cutting/test_cut_wire_to_move.py index c5e9e6e3b..851a20726 100644 --- a/test/cutting/test_cut_wire_to_move.py +++ b/test/cutting/test_cut_wire_to_move.py @@ -10,13 +10,14 @@ # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. -"""Test for the transform_to_move function.""" +"""Tests for single qubit wire cutting functions.""" from __future__ import annotations -from pytest import fixture, mark +from pytest import fixture, mark, raises from qiskit.circuit import QuantumCircuit, QuantumRegister, Qubit, ClassicalRegister +from qiskit.quantum_info import PauliList from circuit_knitting.cutting.instructions import Move, CutWire -from circuit_knitting.cutting import transform_cuts_to_moves +from circuit_knitting.cutting import transform_cuts_to_moves, expand_observables @fixture @@ -323,3 +324,75 @@ def test_creg(request, sample_circuit): final_circuit.cregs, ): assert sample_creg.size == final_creg.size + + +class TestExpandObservables: + def test_expand_observables(self): + qc0 = QuantumCircuit(3) + qc1 = QuantumCircuit() + qc1.add_bits( + [ + qc0.qubits[0], + Qubit(), + Qubit(), + qc0.qubits[1], + qc0.qubits[2], + Qubit(), + ] + ) + observables_in = PauliList( + [ + "XYZ", + "iIXZ", + "-YYZ", + "-iZZZ", + ] + ) + observables_expected = PauliList( + [ + "IXYIIZ", + "iIIXIIZ", + "-IYYIIZ", + "-iIZZIIZ", + ] + ) + observables_out = expand_observables(observables_in, qc0, qc1) + assert observables_out == observables_expected + + def test_with_zero_qubits(self): + qc0 = QuantumCircuit() + qc1 = QuantumCircuit(3) + observables_in = PauliList(["", ""]) + observables_expected = PauliList(["III"] * 2) + observables_out = expand_observables(observables_in, qc0, qc1) + assert observables_out == observables_expected + + def test_with_mismatched_qubit_count(self): + qc0 = QuantumCircuit(3) + qc1 = QuantumCircuit(4) + obs = PauliList(["IZIZ"]) + with raises(ValueError) as e_info: + expand_observables(obs, qc0, qc1) + assert ( + e_info.value.args[0] + == "The `observables` and `original_circuit` must have the same number of qubits. (4 != 3)" + ) + + def test_with_non_subset(self): + qc0 = QuantumCircuit(3) + qc1 = QuantumCircuit() + qc1.add_bits( + [ + qc0.qubits[0], + Qubit(), + qc0.qubits[1], + Qubit(), + ] + ) + obs = PauliList(["IZZ"]) + with raises(ValueError) as e_info: + expand_observables(obs, qc0, qc1) + assert ( + e_info.value.args[0] + == "The 2-th qubit of the `original_circuit` cannot be found in the `final_circuit`." + ) From 5ecd0237a500d02cbc415c19afe657b33ab7600b Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Wed, 16 Aug 2023 19:08:22 -0700 Subject: [PATCH 02/15] Don't unpack the result of `partition_problem` --- docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb index 3e7467ca7..b8cdeb364 100644 --- a/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb +++ b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb @@ -216,9 +216,11 @@ "metadata": {}, "outputs": [], "source": [ - "subcircuits, bases, subobservables = partition_problem(\n", + "partitioned_problem = partition_problem(\n", " circuit=qc_1, partition_labels=\"AAAABABBB\", observables=observables_1\n", - ")" + ")\n", + "subcircuits = partitioned_problem.subcircuits\n", + "subobservables = partitioned_problem.subobservables" ] }, { From 11deba57b84cbce96aead42fa64eed272177e123 Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Wed, 16 Aug 2023 19:40:22 -0700 Subject: [PATCH 03/15] Use automatic `partition_labels` in new `CutWire` how-to --- circuit_knitting/cutting/__init__.py | 6 ++-- circuit_knitting/cutting/cut_wire_to_move.py | 30 ++++++++++++++++-- .../how-tos/how_to_specify_cut_wires.ipynb | 10 +++--- test/cutting/test_cut_wire_to_move.py | 31 ++++++++++++++----- 4 files changed, 58 insertions(+), 19 deletions(-) diff --git a/circuit_knitting/cutting/__init__.py b/circuit_knitting/cutting/__init__.py index 1bf74b68c..fa4c489eb 100644 --- a/circuit_knitting/cutting/__init__.py +++ b/circuit_knitting/cutting/__init__.py @@ -21,7 +21,7 @@ :toctree: ../stubs/ :nosignatures: - transform_cuts_to_moves + cut_wires expand_observables partition_circuit_qubits partition_problem @@ -88,7 +88,7 @@ ) from .cutting_evaluation import execute_experiments, CuttingExperimentResults from .cutting_reconstruction import reconstruct_expectation_values -from .cut_wire_to_move import transform_cuts_to_moves, expand_observables +from .cut_wire_to_move import cut_wires, expand_observables __all__ = [ "partition_circuit_qubits", @@ -99,6 +99,6 @@ "reconstruct_expectation_values", "PartitionedCuttingProblem", "CuttingExperimentResults", - "transform_cuts_to_moves", + "cut_wires", "expand_observables", ] diff --git a/circuit_knitting/cutting/cut_wire_to_move.py b/circuit_knitting/cutting/cut_wire_to_move.py index 06824682c..64e7733f9 100644 --- a/circuit_knitting/cutting/cut_wire_to_move.py +++ b/circuit_knitting/cutting/cut_wire_to_move.py @@ -13,16 +13,34 @@ """Function to transform a :class:`.CutWire` instruction to a :class:`.Move` instruction.""" from __future__ import annotations +from typing import Callable from itertools import groupby import numpy as np -from qiskit.circuit import Qubit, QuantumCircuit +from qiskit.circuit import Qubit, QuantumCircuit, Operation from qiskit.circuit.exceptions import CircuitError from qiskit.quantum_info import PauliList from circuit_knitting.cutting.instructions.move import Move +from circuit_knitting.cutting.qpd.instructions import TwoQubitQPDGate -def transform_cuts_to_moves(circuit: QuantumCircuit, /) -> QuantumCircuit: +def cut_wires(circuit: QuantumCircuit, /) -> QuantumCircuit: + """Transform all :class:`.CutWire` instructions in a circuit to :class:`.Move` instructions marked for cutting. + + The returned circuit will have one newly allocated qubit for every :class:`.CutWire` instruction. + + Args: + circuit: Original circuit with :class:`.CutWire` instructions + + Returns: + circuit: New circuit with :class:`.CutWire` instructions replaced by :class:`.Move` instructions wrapped in :class:`TwoQubitQPDGate`\ s + """ + return _transform_cut_wires( + circuit, lambda: TwoQubitQPDGate.from_instruction(Move()) + ) + + +def _transform_cuts_to_moves(circuit: QuantumCircuit, /) -> QuantumCircuit: """Transform all :class:`.CutWire` instructions in a circuit to :class:`.Move` instructions. Args: @@ -31,6 +49,12 @@ def transform_cuts_to_moves(circuit: QuantumCircuit, /) -> QuantumCircuit: Returns: circuit: New circuit with :class:`.CutWire` instructions replaced by :class`.Move` instructions """ + return _transform_cut_wires(circuit, Move) + + +def _transform_cut_wires( + circuit: QuantumCircuit, factory: Callable[[], Operation], / +) -> QuantumCircuit: new_circuit, mapping = _circuit_structure_mapping(circuit) for instructions in circuit.data: @@ -39,7 +63,7 @@ def transform_cuts_to_moves(circuit: QuantumCircuit, /) -> QuantumCircuit: if instructions in circuit.get_instructions("cut_wire"): # Replace cut_wire with move instruction new_circuit.compose( - other=Move(), + other=factory(), qubits=[mapping[gate_index[0]], mapping[gate_index[0]] + 1], inplace=True, ) diff --git a/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb index b8cdeb364..a762a1173 100644 --- a/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb +++ b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb @@ -29,7 +29,7 @@ ")\n", "\n", "from circuit_knitting.cutting.instructions import CutWire\n", - "from circuit_knitting.cutting import transform_cuts_to_moves, expand_observables" + "from circuit_knitting.cutting import cut_wires, expand_observables" ] }, { @@ -161,7 +161,7 @@ } ], "source": [ - "qc_1 = transform_cuts_to_moves(qc_0)\n", + "qc_1 = cut_wires(qc_0)\n", "qc_1.draw(\"mpl\")" ] }, @@ -217,7 +217,7 @@ "outputs": [], "source": [ "partitioned_problem = partition_problem(\n", - " circuit=qc_1, partition_labels=\"AAAABABBB\", observables=observables_1\n", + " circuit=qc_1, observables=observables_1\n", ")\n", "subcircuits = partitioned_problem.subcircuits\n", "subobservables = partitioned_problem.subobservables" @@ -282,7 +282,7 @@ } ], "source": [ - "subcircuits[\"A\"].draw(\"mpl\")" + "subcircuits[0].draw(\"mpl\")" ] }, { @@ -304,7 +304,7 @@ } ], "source": [ - "subcircuits[\"B\"].draw(\"mpl\")" + "subcircuits[1].draw(\"mpl\")" ] }, { diff --git a/test/cutting/test_cut_wire_to_move.py b/test/cutting/test_cut_wire_to_move.py index 851a20726..f5215c34f 100644 --- a/test/cutting/test_cut_wire_to_move.py +++ b/test/cutting/test_cut_wire_to_move.py @@ -17,7 +17,9 @@ from qiskit.circuit import QuantumCircuit, QuantumRegister, Qubit, ClassicalRegister from qiskit.quantum_info import PauliList from circuit_knitting.cutting.instructions import Move, CutWire -from circuit_knitting.cutting import transform_cuts_to_moves, expand_observables +from circuit_knitting.cutting.qpd.instructions import TwoQubitQPDGate +from circuit_knitting.cutting import cut_wires, expand_observables +from circuit_knitting.cutting.cut_wire_to_move import _transform_cuts_to_moves @fixture @@ -205,9 +207,9 @@ def resulting_circuit4() -> tuple[QuantumCircuit, list[int]]: ("circuit4", "resulting_circuit4"), ], ) -def test_transform_cuts_to_moves(request, sample_circuit, resulting_circuit): +def test__transform_cuts_to_moves(request, sample_circuit, resulting_circuit): """Tests the transformation of CutWire to Move instruction.""" - assert request.getfixturevalue(resulting_circuit)[0] == transform_cuts_to_moves( + assert request.getfixturevalue(resulting_circuit)[0] == _transform_cuts_to_moves( request.getfixturevalue(sample_circuit) ) @@ -226,7 +228,7 @@ def test_circuit_mapping(request, sample_circuit, resulting_circuit): sample_circuit = request.getfixturevalue(sample_circuit) resulting_mapping = request.getfixturevalue(resulting_circuit)[1] - final_circuit = transform_cuts_to_moves(sample_circuit) + final_circuit = _transform_cuts_to_moves(sample_circuit) final_mapping = [ final_circuit.find_bit(qubit).index for qubit in sample_circuit.qubits ] @@ -249,7 +251,7 @@ def test_circuit_mapping(request, sample_circuit, resulting_circuit): def test_qreg_name_num(request, sample_circuit): """Tests the number and name of qregs in initial and final circuits.""" sample_circuit = request.getfixturevalue(sample_circuit) - final_circuit = transform_cuts_to_moves(sample_circuit) + final_circuit = _transform_cuts_to_moves(sample_circuit) # Tests number of qregs in initial and final circuits assert len(sample_circuit.qregs) == len(final_circuit.qregs) @@ -273,7 +275,7 @@ def test_qreg_name_num(request, sample_circuit): def test_qreg_size(request, sample_circuit): """Tests the size of qregs in initial and final circuits.""" sample_circuit = request.getfixturevalue(sample_circuit) - final_circuit = transform_cuts_to_moves(sample_circuit) + final_circuit = _transform_cuts_to_moves(sample_circuit) # Tests size of qregs in initial and final circuits for sample_qreg, final_qreg in zip( @@ -295,7 +297,7 @@ def test_qreg_size(request, sample_circuit): def test_circuit_width(request, sample_circuit): """Tests the width of the initial and final circuits.""" sample_circuit = request.getfixturevalue(sample_circuit) - final_circuit = transform_cuts_to_moves(sample_circuit) + final_circuit = _transform_cuts_to_moves(sample_circuit) total_cut_wire = len(sample_circuit.get_instructions("cut_wire")) # Tests width of initial and final circuit @@ -314,7 +316,7 @@ def test_circuit_width(request, sample_circuit): def test_creg(request, sample_circuit): """Tests the number and size of cregs in the initial and final circuits.""" sample_circuit = request.getfixturevalue(sample_circuit) - final_circuit = transform_cuts_to_moves(sample_circuit) + final_circuit = _transform_cuts_to_moves(sample_circuit) # Tests number of cregs in initial and final circuits assert len(sample_circuit.cregs) == len(final_circuit.cregs) @@ -326,6 +328,19 @@ def test_creg(request, sample_circuit): assert sample_creg.size == final_creg.size +def test_cut_wires(): + qc = QuantumCircuit(2) + qc.h(0) + qc.h(1) + qc.append(CutWire(), [1]) + qc.s(0) + qc.s(1) + qc_out = cut_wires(qc) + qpd_gate = qc_out.data[2].operation + assert isinstance(qpd_gate, TwoQubitQPDGate) + assert qpd_gate.label == "cut_move" + + class TestExpandObservables: def test_expand_observables(self): qc0 = QuantumCircuit(3) From 0d08b59f1f66c464e066909e2f4c332871308783 Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Thu, 17 Aug 2023 13:48:27 -0700 Subject: [PATCH 04/15] peer review https://github.com/Qiskit-Extensions/circuit-knitting-toolbox/pull/368/files#r1297182836 --- circuit_knitting/cutting/cut_wire_to_move.py | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/circuit_knitting/cutting/cut_wire_to_move.py b/circuit_knitting/cutting/cut_wire_to_move.py index 06824682c..1fff53b6f 100644 --- a/circuit_knitting/cutting/cut_wire_to_move.py +++ b/circuit_knitting/cutting/cut_wire_to_move.py @@ -14,12 +14,13 @@ from __future__ import annotations from itertools import groupby -import numpy as np +import numpy as np from qiskit.circuit import Qubit, QuantumCircuit from qiskit.circuit.exceptions import CircuitError from qiskit.quantum_info import PauliList -from circuit_knitting.cutting.instructions.move import Move + +from .instructions.move import Move def transform_cuts_to_moves(circuit: QuantumCircuit, /) -> QuantumCircuit: From b2f84b8b0a09074237cbd54bc839fc2f4183f938 Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Thu, 17 Aug 2023 16:53:27 -0400 Subject: [PATCH 05/15] Apply suggestions from code review Co-authored-by: Caleb Johnson --- circuit_knitting/cutting/cut_wire_to_move.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/circuit_knitting/cutting/cut_wire_to_move.py b/circuit_knitting/cutting/cut_wire_to_move.py index 1fff53b6f..da2874431 100644 --- a/circuit_knitting/cutting/cut_wire_to_move.py +++ b/circuit_knitting/cutting/cut_wire_to_move.py @@ -117,10 +117,10 @@ def expand_observables( Args: observables: Observables corresponding to ``original_circuit`` original_circuit: Original circuit - final_circuit: Final circuit, whose qubits the original ``observables`` should be expanded to. + final_circuit: Final circuit, whose qubits the original ``observables`` should be expanded to Returns: - New observables, appropriate for the ``final_circuit``. + New :math:`N`-qubit observables which are compatible with the :math:`N`-qubit ``final_circuit`` Raises: ValueError: ``observables`` and ``original_circuit`` have different number of qubits. From a5ebfb8abe937d1fa84fb847c0e7e7672183a7b8 Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Thu, 17 Aug 2023 13:56:16 -0700 Subject: [PATCH 06/15] Clarify superset of `Qubit`s --- circuit_knitting/cutting/cut_wire_to_move.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/circuit_knitting/cutting/cut_wire_to_move.py b/circuit_knitting/cutting/cut_wire_to_move.py index da2874431..583fe4dac 100644 --- a/circuit_knitting/cutting/cut_wire_to_move.py +++ b/circuit_knitting/cutting/cut_wire_to_move.py @@ -97,7 +97,7 @@ def expand_observables( ) -> PauliList: """Expand observable(s) according to the qubit mapping between ``original_circuit`` and ``final_circuit``. - The qubits on ``final_circuit`` must be a superset of those on + The :class:`.Qubit`\ s on ``final_circuit`` must be a superset of those on ``original_circuit``. Given a :class:`.PauliList` of observables, this function returns new From ed3d568df23a667cfb809445a11795e8e1725f29 Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Thu, 17 Aug 2023 17:48:43 -0700 Subject: [PATCH 07/15] Fix lint --- circuit_knitting/cutting/cut_wire_to_move.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/circuit_knitting/cutting/cut_wire_to_move.py b/circuit_knitting/cutting/cut_wire_to_move.py index 583fe4dac..bf79bd4f1 100644 --- a/circuit_knitting/cutting/cut_wire_to_move.py +++ b/circuit_knitting/cutting/cut_wire_to_move.py @@ -95,7 +95,7 @@ def expand_observables( final_circuit: QuantumCircuit, /, ) -> PauliList: - """Expand observable(s) according to the qubit mapping between ``original_circuit`` and ``final_circuit``. + r"""Expand observable(s) according to the qubit mapping between ``original_circuit`` and ``final_circuit``. The :class:`.Qubit`\ s on ``final_circuit`` must be a superset of those on ``original_circuit``. From 9dc760e68b09ac5507e12dbc57ab88c685d1d9f6 Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Thu, 17 Aug 2023 21:21:20 -0700 Subject: [PATCH 08/15] arXiv -> link --- docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb index b8cdeb364..f45c893c2 100644 --- a/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb +++ b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb @@ -39,7 +39,7 @@ "source": [ "### Prepare a circuit for cutting\n", "\n", - "As in the [tutorial for wire cutting](../tutorials/03_wire_cutting_via_move_instruction.ipynb), we have used a circuit inspired by Fig. 1(a) of arXiv:2302.03366v1. The cut locations are marked manually here with `CutWire` instructions." + "As in the [tutorial for wire cutting](../tutorials/03_wire_cutting_via_move_instruction.ipynb), we have used a circuit inspired by Fig. 1(a) of [arXiv:2302.03366v1](https://arxiv.org/abs/2302.03366v1). The cut locations are marked manually here with `CutWire` instructions." ] }, { From a3f1afd959e9ec80f27fca6e94a57efc64773a01 Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Fri, 18 Aug 2023 06:33:11 -0700 Subject: [PATCH 09/15] Run notebook cells --- .../how-tos/how_to_specify_cut_wires.ipynb | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb index 5d33e4346..50307ed77 100644 --- a/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb +++ b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb @@ -150,7 +150,7 @@ "outputs": [ { "data": { - "image/png": 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", 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" ] @@ -248,8 +248,8 @@ { "data": { "text/plain": [ - "{'A': PauliList(['IIIII', 'ZIIII', 'IIIIZ']),\n", - " 'B': PauliList(['ZIII', 'IIII', 'IIII'])}" + "{0: PauliList(['IIIII', 'ZIIII', 'IIIIZ']),\n", + " 1: PauliList(['ZIII', 'IIII', 'IIII'])}" ] }, "execution_count": 8, @@ -352,10 +352,10 @@ "name": "stdout", "output_type": "stream", "text": [ - "Reconstructed expectation values: [0.16293341, 0.69796044, 0.71675336]\n", + "Reconstructed expectation values: [0.17901284, 0.70971423, 0.68885177]\n", "Exact expectation values: [0.1767767, 0.70710678, 0.70710678]\n", - "Errors in estimation: [-0.01384329, -0.00914634, 0.00964658]\n", - "Relative errors in estimation: [-0.07830945, -0.01293488, 0.01364233]\n" + "Errors in estimation: [0.00223614, 0.00260745, -0.01825501]\n", + "Relative errors in estimation: [0.01264952, 0.00368749, -0.02581648]\n" ] } ], From e4c4ce4e2945a4647c57b7b957ca273ca87952cd Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Fri, 18 Aug 2023 06:47:10 -0700 Subject: [PATCH 10/15] Update prose in how-to --- docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb index 50307ed77..5da0f3a7a 100644 --- a/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb +++ b/docs/circuit_cutting/how-tos/how_to_specify_cut_wires.ipynb @@ -137,9 +137,9 @@ "source": [ "### Transform cuts to moves\n", "\n", - "The next step is to transform each `CutWire` into a `Move`. An additional qubit is added to the circuit for each `CutWire` in the input circuit.\n", + "The next step is to call `cut_wires`, which transforms each `CutWire` into a `TwoQubitQPDGate` which wraps a `Move` instruction. An additional qubit is added to the circuit for each `CutWire` in the input circuit.\n", "\n", - "Notice that, unlike in the [wire cutting tutorial](../tutorials/03_wire_cutting_via_move_instruction.ipynb), this function does not result in the _re_-use of a qubit. Because any method for qubit re-use is based on heuristics, this function naively allocates an additional qubit for each cut. Users wishing to re-use qubits might wish to experiment with [qiskit-qubit-reuse](https://github.com/qiskit-community/qiskit-qubit-reuse)." + "Notice that, unlike in the [wire cutting tutorial](../tutorials/03_wire_cutting_via_move_instruction.ipynb), where `Move` operations were placed manually, this function does not result in the _re_-use of a qubit. Because any method for qubit re-use is based on heuristics, this function naively allocates an additional qubit for each cut. Users wishing to re-use qubits might wish to experiment with [qiskit-qubit-reuse](https://github.com/qiskit-community/qiskit-qubit-reuse)." ] }, { @@ -206,7 +206,7 @@ "source": [ "### Separate the circuit and observables\n", "\n", - "In order to partition the circuit, we must specify `partition_labels` based on the connectivity of the circuit. In the future, we expect to provide a way for this to be determined automatically, as it is technically redundant with the information contained by the original circuit with `CutWire` instructions (see PR [#367](https://github.com/Qiskit-Extensions/circuit-knitting-toolbox/pull/367))." + "In this case, `partition_labels` need not be passed to `partition_problem`, as the labels can be determined automatically from the connectivity of the circuit." ] }, { From c8424a02fe97e0007664ca45dd59caf7aa9f058b Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Fri, 18 Aug 2023 06:59:23 -0700 Subject: [PATCH 11/15] Update text in wire cutting tutorial to mention how-to --- .../tutorials/03_wire_cutting_via_move_instruction.ipynb | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/docs/circuit_cutting/tutorials/03_wire_cutting_via_move_instruction.ipynb b/docs/circuit_cutting/tutorials/03_wire_cutting_via_move_instruction.ipynb index 758852220..5eb72d971 100644 --- a/docs/circuit_cutting/tutorials/03_wire_cutting_via_move_instruction.ipynb +++ b/docs/circuit_cutting/tutorials/03_wire_cutting_via_move_instruction.ipynb @@ -127,9 +127,11 @@ "source": [ "### Create a new circuit where `Move` instructions have been placed at the desired cut locations\n", "\n", - "Given the above circuit, we would like to place two wire cuts on the middle qubit line, so that the circuit can separate into two circuits of four qubits each. One way to do this (currently, the only way) is to place two-qubit `Move` instructions that move the state from one qubit wire to another. A `Move` instruction is conceptually equivalent to a reset operation on the second qubit, followed by a SWAP gate. The effect of this instruction is to transfer the state of the first (source) qubit to the second (detination) qubit, while discarding the incoming state of the second qubit. For this to work as intended, it is important that the second (destination) qubit share no entanglement with the remainder of the system; otherwise, the reset operation will cause the state of the remainder of the system to be partially collapsed.\n", + "Given the above circuit, we would like to place two wire cuts on the middle qubit line, so that the circuit can separate into two circuits of four qubits each. One way to do this is to manually place two-qubit `Move` instructions that move the state from one qubit wire to another. A `Move` instruction is conceptually equivalent to a reset operation on the second qubit, followed by a SWAP gate. The effect of this instruction is to transfer the state of the first (source) qubit to the second (detination) qubit, while discarding the incoming state of the second qubit. For this to work as intended, it is important that the second (destination) qubit share no entanglement with the remainder of the system; otherwise, the reset operation will cause the state of the remainder of the system to be partially collapsed.\n", "\n", - "Here, we build a new circuit with one additional qubit and the `Move` operations in place. In this example, we are able to reuse a qubit: the source qubit of the first `Move` becomes the destination qubit of the second `Move` operation." + "Here, we build a new circuit with one additional qubit and the `Move` operations in place. In this example, we are able to reuse a qubit: the source qubit of the first `Move` becomes the destination qubit of the second `Move` operation.\n", + "\n", + "Note: As an alternative to working directly with `Move` instructions, one may choose to mark wire cuts using a single-qubit `CutWire` instruction. The `cut_wires` function exists to transform such cuts to `Move` instructions on newly allocated qubits. However, in contrast to the manual method, this automatic method does not allow for the re-use of qubit wires. See the `CutWire` [how-to guide](../how-tos/how_to_specify_cut_wires.ipynb) for details." ] }, { From 0b759a464cd71fdc8a63e6956ec6e0743a9ff449 Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Fri, 18 Aug 2023 07:03:35 -0700 Subject: [PATCH 12/15] Forgot the save before committing --- .../tutorials/03_wire_cutting_via_move_instruction.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/circuit_cutting/tutorials/03_wire_cutting_via_move_instruction.ipynb b/docs/circuit_cutting/tutorials/03_wire_cutting_via_move_instruction.ipynb index 5eb72d971..659cc27e9 100644 --- a/docs/circuit_cutting/tutorials/03_wire_cutting_via_move_instruction.ipynb +++ b/docs/circuit_cutting/tutorials/03_wire_cutting_via_move_instruction.ipynb @@ -131,7 +131,7 @@ "\n", "Here, we build a new circuit with one additional qubit and the `Move` operations in place. In this example, we are able to reuse a qubit: the source qubit of the first `Move` becomes the destination qubit of the second `Move` operation.\n", "\n", - "Note: As an alternative to working directly with `Move` instructions, one may choose to mark wire cuts using a single-qubit `CutWire` instruction. The `cut_wires` function exists to transform such cuts to `Move` instructions on newly allocated qubits. However, in contrast to the manual method, this automatic method does not allow for the re-use of qubit wires. See the `CutWire` [how-to guide](../how-tos/how_to_specify_cut_wires.ipynb) for details." + "Note: As an alternative to working directly with `Move` instructions, one may choose to mark wire cuts using a single-qubit `CutWire` instruction. The `cut_wires` function exists to transform `CutWire`s to `Move` instructions on newly allocated qubits. However, in contrast to the manual method, this automatic method does not allow for the re-use of qubit wires. See the `CutWire` [how-to guide](../how-tos/how_to_specify_cut_wires.ipynb) for details." ] }, { From 8711b1148475892739203d2dbd3d0a15169b5366 Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Fri, 18 Aug 2023 07:05:50 -0700 Subject: [PATCH 13/15] Add link to Lukas Brenner, Christophe Piveteau, David Sutter paper --- circuit_knitting/cutting/cut_wire_to_move.py | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/circuit_knitting/cutting/cut_wire_to_move.py b/circuit_knitting/cutting/cut_wire_to_move.py index 26c07c910..31fb841af 100644 --- a/circuit_knitting/cutting/cut_wire_to_move.py +++ b/circuit_knitting/cutting/cut_wire_to_move.py @@ -30,6 +30,11 @@ def cut_wires(circuit: QuantumCircuit, /) -> QuantumCircuit: The returned circuit will have one newly allocated qubit for every :class:`.CutWire` instruction. + See Sec. 3 and Appendix A of `2302.03366v1 + `__ for more information about the two + different representations of wire cuts: single-qubit (:class:`.CutWire`) + vs. two-qubit (:class:`.Move`). + Args: circuit: Original circuit with :class:`.CutWire` instructions From 24a653a687cf39d7e30bc32037bc21d9907829f5 Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Fri, 18 Aug 2023 07:11:12 -0700 Subject: [PATCH 14/15] Rename `cut_wire_to_move` to `wire_cutting_transforms` --- circuit_knitting/cutting/__init__.py | 2 +- .../cutting/{cut_wire_to_move.py => wire_cutting_transforms.py} | 0 ...test_cut_wire_to_move.py => test_wire_cutting_transforms.py} | 2 +- 3 files changed, 2 insertions(+), 2 deletions(-) rename circuit_knitting/cutting/{cut_wire_to_move.py => wire_cutting_transforms.py} (100%) rename test/cutting/{test_cut_wire_to_move.py => test_wire_cutting_transforms.py} (99%) diff --git a/circuit_knitting/cutting/__init__.py b/circuit_knitting/cutting/__init__.py index d85886bfb..b8f65f9eb 100644 --- a/circuit_knitting/cutting/__init__.py +++ b/circuit_knitting/cutting/__init__.py @@ -88,7 +88,7 @@ ) from .cutting_evaluation import execute_experiments, CuttingExperimentResults from .cutting_reconstruction import reconstruct_expectation_values -from .cut_wire_to_move import cut_wires, expand_observables +from .wire_cutting_transforms import cut_wires, expand_observables __all__ = [ "partition_circuit_qubits", diff --git a/circuit_knitting/cutting/cut_wire_to_move.py b/circuit_knitting/cutting/wire_cutting_transforms.py similarity index 100% rename from circuit_knitting/cutting/cut_wire_to_move.py rename to circuit_knitting/cutting/wire_cutting_transforms.py diff --git a/test/cutting/test_cut_wire_to_move.py b/test/cutting/test_wire_cutting_transforms.py similarity index 99% rename from test/cutting/test_cut_wire_to_move.py rename to test/cutting/test_wire_cutting_transforms.py index f5215c34f..c504998f6 100644 --- a/test/cutting/test_cut_wire_to_move.py +++ b/test/cutting/test_wire_cutting_transforms.py @@ -19,7 +19,7 @@ from circuit_knitting.cutting.instructions import Move, CutWire from circuit_knitting.cutting.qpd.instructions import TwoQubitQPDGate from circuit_knitting.cutting import cut_wires, expand_observables -from circuit_knitting.cutting.cut_wire_to_move import _transform_cuts_to_moves +from circuit_knitting.cutting.wire_cutting_transforms import _transform_cuts_to_moves @fixture From bebe5ffced12c192bb09b18d3ebbc15dc599265f Mon Sep 17 00:00:00 2001 From: Jim Garrison Date: Fri, 18 Aug 2023 15:46:44 -0700 Subject: [PATCH 15/15] Fix double underscore https://github.com/Qiskit-Extensions/circuit-knitting-toolbox/pull/370#discussion_r1298843568 --- test/cutting/test_wire_cutting_transforms.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test/cutting/test_wire_cutting_transforms.py b/test/cutting/test_wire_cutting_transforms.py index c504998f6..2869dad8f 100644 --- a/test/cutting/test_wire_cutting_transforms.py +++ b/test/cutting/test_wire_cutting_transforms.py @@ -207,7 +207,7 @@ def resulting_circuit4() -> tuple[QuantumCircuit, list[int]]: ("circuit4", "resulting_circuit4"), ], ) -def test__transform_cuts_to_moves(request, sample_circuit, resulting_circuit): +def test_transform_cuts_to_moves(request, sample_circuit, resulting_circuit): """Tests the transformation of CutWire to Move instruction.""" assert request.getfixturevalue(resulting_circuit)[0] == _transform_cuts_to_moves( request.getfixturevalue(sample_circuit)